How are exoplanetary atmosphere compositional spectra distinguished from those of the parent star(s), from the composition of the planetary surface or any other factor? Is it actually possible to determine the atmospheric composition precisely using this method?

Are there any specific examples of such an analysis having been performed on an exoplanet?

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In theory one should just be able to determine the difference between the spectra during the exoplanet's eclipse of the star and the spectra of the star alone, but in reality equipment is not precise enough for this. To remedy this problem, the analysis is integrated over many eclipses. Some other calibrations are made as well which you can read more about in the paper A Spitzer Spectrum of the Exoplanet HD 189733b.